MATHEMATICAL MODEL FOR GREENHOUSE HEATING BY …

BIOLOGICAL ENGINEERING

Misr J. Ag. Eng., July 2011 - 734 -

MATHEMATICAL MODEL FOR GREENHOUSE

HEATING BY WASTE HEAT FROM

BIOGAS FUEL ENGINE

Gamea, G. R.* Abd El-Maksoud, M. A.* Omar, M. N.**

ABSTRACT

A mathematical model consisting of algebraic equations was developed

for greenhouse heating integrated with a heater exchanger. The works on

the principal of utilizing the waste heat from the biogas fuel engine. The

equations were used by MATLAB program for four components of the

greenhouse, cover, inside air, plant and soil. It was assumed that the

greenhouse air is well mixed. Thermal properties of construction

materials are constant and solar radiations pass through cover without

absorption. The analysis is based on the energy balance equations for

different components of the greenhouse. The model is developed to

calculate the hourly temperatures of greenhouse components under

climatic parameters. Experimental validation of the developed model is

carried out in Ostobary, Shibin El-Kom, Minofiya latitude angle is 30o 54

'

north during November 2009 to March 2010. The results of computer

model (predicted data) were compared with the experimental results. The

minimum correlation coefficients between values were 0.970, 0.975,

0.970, 0.977 and 0.818 for air, soil, cover, plant and relative humidity

respectively. The minimum temperatures were 13, 12.77, 13.57 and 15.8 oC for air, cover, plant and soil. Good agreement between the predicted

and measured values was obtained during the entire modelling period.

This means that the model can be used to predict a thermal performance

of the greenhouse elements in a wide range of solar radiation and

temperatures. Using waste heat as an input for greenhouse operations is a

new mechanism for reducing operating costs.

Keywords: Biogas, Model, Waste, Greenhouse, Heating, Exchanger.

*Associate professor of Agricultural Engineering, Faculty of

Agriculture, Minofiya University.

**Associate Lecturer of Agricultural Engineering, Faculty of

Agriculture, Minofiya University.

Misr J. Ag. Eng., 28(3): 734 - 758



INTRODUCTION

he world population is expected to rise in the next years. In order

to feed these people, there is a need to increase the quantity of

food product in sustainable way. Greenhouses allow producers to

grow plants at time and location when it would be impossible to grow

outside because of the adverse climate, pests and diseases. In order to

achieve maximum returns from greenhouse cultivation, it is important to

maintain an environment that promotes optimum plant growth and

production all year round. The growth factors namely: light, temperature,

humidity and air composition should be delivered and maintained at

optimal levels. To maintain this optimum growing environment,

greenhouses ought to allow high light transmittance, heat consumption,

sufficient ventilation efficiency, low construction and operating costs

Mutwiwa (2007). To be able to utilize greenhouses to produce

agricultural products outside the normal cultivation season, it is necessary

to heat them, particularly during the cold seasons. Applying heating in the

greenhouses has an important effect on the yield as well as on the quality

and on the cultivation time of the products as well. As energy costs are

increasing, many greenhouse operators are re-evaluating energy

consumption and savings strategies. In most cases, updating older heating

systems to more efficient units in addition to the use of double layer

glazing, insulation materials, and energy curtains significantly reduces

fuel consumption. But the energy crisis of the next few years is the

shortage of fuel for the daily needs of millions of people. Simple biogas is

intended to help solve this problem Gautam et al. (2007).

Nomenclature

m2 cover surface area Aco

m2 plant surface area Apl

m2 soil surface area Aso

- cloudiness factor in the range from 0 to 1 b

m thickness of the soil L

kg mass of water wm

h selected simulation time n

kPa atmospheric pressure ap

T



kpa water vapour pressure Pwv

kPa saturated vapour pressure wvsp

kPa saturation vapor pressure at the dry- bulb

temperature wvsP

kPa saturation vapor pressure at the wet- bulb

temperature

*

wvsP

Wm-2

thermal heat loss from greenhouse air due to

ventilation ventQ

Wm-2

thermal heat loss from greenhouse soil due to

evaporation evapQ

Wm-2

thermal radiation from the heating system heatingQ

Wm-2

thermal radiation loss from cover to sky skycordQ

Wm-2

total thermal energy transferred from heating

system hQ

Wm-2

radiation exchange between the cover and

plant plcordQ

Wm-2

radiation exchange between the cover and soil socordQ

Wm-2

radiation exchange between the plant and soil soplrdQ

Wm-2

rate of energy loss from the soil to the ground

depth cdQ

Wm-2

heat flow due to transpiration transQ

Wm-2

heat flux due to conduction from soil to air socdQ

Wm-2

heat flux due to convection from cover to air coCVQ

Wm-2

heat flux due to convection from plant to air plCVQ

Wm-2

latent heat LtQ

Wm-2

latent heat of condensation condenQ

Wm-2

sensible heat SiQ

Wm-2

solar energy absorbed by plant surface plGQ

Wm-2

solar energy absorbed by soil surface soGQ

Whg-1

latent heat of vaporisation r

[% relative humidity RH

Wm-2

solar radiant energy outside the greenhouse tS

oC inside air temperature Tair

oC design interior air temperature in the night Tin



oC outside ambient air temperature Tout

K leaf surface temperature Tpl

K sky temperature Tsky

K temperature at the surface soil Tso – x=0

K temperature at the soil depth Tso – x=l: oC cover surface temperature co

oC dry-bulb temperature tdry,

h simulation time t

m3 greenhouse volume gV

ms-1

wind velocity

kgkg-1

water content of inside greenhouse air insx

kgkg-1

water content of outside greenhouse air outx

kgkg-1

water content of the saturated air satx

kgkg-1

saturation water content at the cover surface

temperature cosatx

kgkg-1

saturation water content at the soil surface

temperature sosatx

kgkg-1

saturation water content at the plant

temperature plsatx

h-1

air exchange number Z

- transmissivity of the cover

Wm-2 o

C -1

coefficient of convective thermal transmission

from cover co

Wm-2 o

C -1


from plant pl

Wm-2 o

C -1


from soil so

Wm-2 0

C-1


from the hot exhaust gas in the pipe to the

greenhouse air h

m-1

constant factor

- effective emissivity between cover surface and

plant copl

- effective emissivity between cover surface and

soil soco,



- effective emissivity between plant surface and

soil sopl,

- emissivity of the cover co

- emissivity of the plant pl

- emissivity of the soil so

Wm-2

K-1

heat transfer coefficient inside the greenhouse ins

- leaf surface absorption Pl

- soil surface absorption g

Wm-2

K-4

Stefan-Boltzmann constant

Wm-1

K-1

thermal conductivity of the soil

Because of the relatively high cost and uncertain availability of fossil

fuels, considerable attention has been given to a new and renewable

energy sources as an alternative means of heating greenhouses Oeztuerk

and Baescetin-celik (2003). Using waste heat as an input for greenhouse

operations is proposed as a mechanism for reducing operating costs.

Because heat is such a major expense for operating greenhouses, the cost

savings associated with obtaining it for free could theoretically be quite

substantial. Internal combustion can be coupled with a generator to

produce electricity. Heat can also be recovered, both from the exhaust gas

and from the engine cooling system with heating efficiencies in the range

60 to 70% Willits et al., (2003). Biogas production is a key technology for

using the agrarian biomass as renewable energy source, and solves the

problem of environmental pollution. High energy yields from agricultural

wastes can be achieved through biogas production. Biogas can be

produced from a wide range of energy crops, animal manures and organic

wastes. Thus, it offers a high flexibility and can be adapted to the specific

needs of contrasting locations and farm managements. After anaerobic

digestion, the digestion residues can be used as a valuable fertilizer for

agricultural crops Amon et al., 2007. The main objective of the study is to

Simulated and validation of a mathematical model for Optimization of

using waste heat from an engine biogas fuel for greenhouse heating.



MATERIALS AND METHODS

2.1 Mathematical modells

The model was designed for evaluation performance the greenhouse that

heating with the exhaust gas from the engine. Heat transfer is energy in

transit due to a temperature difference between two nodes with different

temperatures Oeztuerk (2005). The equations were written for four

components of the greenhouse that’s, cover, inside air, plants surface and

soil surface. The equations were solved using Matlab program. The

temperature of each node is spatially uniform. The thermal radiative,

sensible, latent, and conductive heat fluxes were modelled by

mathematical equations in terms of unknown temperatures and vapour

pressures. The energy balance equations were then developed for each

node in the experimental greenhouse, where the sum of the fluxes at that

node should be zero. The equations were solved by an integrative

procedure to obtain the unknown temperatures and vapour pressures.

Figure (1) shows the model of the heat dynamics for different components

of the greenhouse.

Fig.1: Energy balance and fluxes of the all components of the

greenhouse.

2.1.1 The greenhouse air

In the energy balance of inside air of greenhouse, only the convective heat

transfer is considered. It is assumed that no thermal or solar radiation is



absorbed by the air. The energy balance for the air inside the greenhouse

show in the following equations:

0 venthCOCVSOCVPLCV QQQQQ (1)

Where

airplPLPLCVQ , Wm-2

(2)

airsososoCVQ , Wm-2

(3)

aircococoCVQ , Wm-2

(4)

)()( airgashh TTQ , Wm-2

(5)

The energy removed by ventilation consists of sensible and latent heat.

The net energy flux Qvent from inside to outside due to ventilation through

a ventilation opening can be easily calculated according to Harmanto

(2006) as follows:

rxxCA

ZVQQQ outinsPoutins

g

LtSivent

, Wm-2

(6)

Where Z is the air exchange number and calculated according to Von

Elsner (1982), 25.0 vZ , h-1

(7)

2.1.2 The greenhouse soil

The soil surface gains heat from thermal radiations emitted through

greenhouse cover and absorbed by the soil surface and the thermal

radiation from the heating system. The soil in the greenhouse is

considered a large heat storage element Tantau (1998). It loses heat

through the thermal radiations emitted by the soil surface, conduction

through the soil and convective heat transfer form the soil surface to the

inside air.

0 heatingevapcdsocvsocordsoplrdsoG QQQQQQQ (8)

The soil surface gains heat from thermal radiations emitted through

greenhouse cover and absorbed by the soil surface calculated according

to Singha et al (2006) as follows:



tpgsoG SQ 1 , Wm-2

(9)

44

, sopl

pl

so

soplsoplrdQ

, Wm

-2 (10)

111

1,

sopl

so

pl

sopl

A

A

, - (11)

44

, soco

co

so

socosocordQ

, Wm

-2 (12)

L

Q lxsoxso

socd

0 , Wm

-2 (14)

inssosatsoins

evap xxrcp

Q

, Wm-2

(15)

Absolute humidity xair is defined as the mass of water divided by the mass

of dry air Lewis (1990).

d

w

airm

mx , kg kg

-1 (16)

Air becomes saturated when the water vapour pressure Pwv is equal to the

saturated vapour pressure, at given temperature. Therefore, the absolute

humidity xsat of saturated air is given by the following equation:

wva

wv

airpp

px

29

18, kg kg

-1 (17)

wvsa

wvs

satpp

px

29

18, kg kg

-1 (18)

The following algorithm used for calculating saturation vapour pressure is

limited to the range of temperatures from 0 to 100 °C Taha (2003). The

determination of the saturation vapour pressure is the most important

calculation in specifying moist air properties since all such properties are



considered as a function of the vapour pressure. This equation is

expressed as follows:

3.273

2693882.17exp61078.0

t

tpwvs , kPa (19)

2.1.3 The greenhouse plant

The greenhouse-crop system can be considered as a solar collector

involving both sensible and latent heat exchanges and its thermal

performances can be described in a similar way by using energy balance

equation Seginer and Alberight (1980). Part of the energy absorbed by the

plants is transferred to latent heat due to transpiration. This energy flux

resulting from the plants transpiration was mentioned in following

equation Boulard et al., (1990).

0 transplcvsoplrdcoplrdplG QQQQQ (20)

The heat gains from thermal radiations emitted through greenhouse cover

and absorbed by the plants surface calculated according to Singha (2006)

as follows:

tplplG SQ , Wm-2

(21)

44

, copl

pl

co

coplcoplrdQ

, Wm

-2 (22)

111

1,

copl

co

pl

copl

A

A

, - (23)

insplsatplins

trans xxrcp

Q

, Wm-2

(24)

2.1.4 The greenhouse cover

Energy balance of the cover of greenhouse not includes solar radiations

absorbed by the cover, convective heat transfer between cover and outside

air, convective heat transfer between cover and inside air, thermal

radiation exchange between cover and sky and latent heat transfer to

cover by condensation.



0 condoutaircvinsairCVskycordcoplrdcosord QQQQQQ (25)

44

skycocoskycordQ , Wm-2

(26)

The sky temperature can be calculated according to von Elsner (1983)

equation as follows:

eesky TbTT 26.06.204.212.1 , oC (27)

cosatins

ins

cnden xxrcp

Q

, Wm-2

(28)

2.1.5 Calculation of the inside relative humidity

To calculation the relative humidity (RH) inside greenhouse by the model

we want to calculation the moisture content of the inside air greenhouse

and the saturation vapour pressure. Those are the most important

calculation for RH. The following equations are used to determination the

RH inside greenhouse:-

100wvs

wv

P

PRH , % (29)

2.1.6 Differential equation:

To calculate the temperature of the greenhouse elements (air, soil, plants

and covering material) the following differential equation was used Taha

(2003).

dtQQc

T los

nt

tp

sup

0

1

, k (30)

2.1.7 Model parameters and boundary conditions

Various parameters affect on the behaviour of the model. These

parameters are the typical features of the greenhouse which are divided

into five internal layers: the cover, the internal air, the soil, the plants and

the heating system, and four boundary layers: the solar radiations, the sky,

the external air and the sub-soil. The optimum values obtained by this

study are compared to that found in the literatures it can be seen in table

(1).



Table 1: Literature and optimum values of the parameters

considered in the model.

parameter Literature-

value References

Optimum

values

α inside,Wm-2K-

1

1.5 to 4

1.25 to

10.9

2 to 5

Taha et al ., 2009

Shukla et al.2006

Tantau 1983

3.25 for soil

,4.9 for

cover and

9.3for plant

α inside,Wm-2

K-1

heating pipes

400 to

4380 Tantau 1983 900

α outside,Wm-2

K-1

43 to 59

4 to 30

4 to 34

Kumari et al 2003

Taha, 2003

Tantau 1983,

29

Cp(air),Wh Kg-1

K-1

0.280 He et al., 2009 0.28

Cp(so),Wh Kg-1

K-1

0.51

0.236 to

0.4

Singha, G. et al.

2006

Elsheikh, 2001

0.32

Cp(pl),Wh Kg-1

K-1

0.9 to 1.3 Singha, G. et al.

2006 1.16

λ(so),Wm-1

K-1

0.8 to 2.3

0.8

Taha, 2003,

Elsheikh 2001

Singha, G. et al.

2006

0.8

φCm,- 0.25 to 0.4 Taha, 2003,

Elsheikh, 2001 0.25-0.40

φso ,- 0.9 Ghosal, M.K.

Tiwari, G.N. 2006 0.9

φ sk ,- 1

0.5 to 1.0

ELSheikh 2001

Strauch 1985 1

ζ (So) ,- 0.0 to 0.8 Strauch 1985 0.60

ζ (p) , - 0.40 Taha, 2003 0.40



2.2Experimental setup

The experimental setup used in this work shows in the schematic diagram

figure (2).

Fig.2: Schematic diagram show the experimental setup.

2.2.1 Greenhouse construction and roof material

To achieve the objectives of the study, a Quonset greenhouse with heat

exchanger unit constructed were carried out during winter 2009/2010

season and installed in Ostobary village, Shibin El-Kom, Minofiya

(Geographically, the chosen place’s latitude angle is 30o 54' degrees), was

used. The direction of the greenhouse was east–west to take the maximum

benefit from the sun during winter. The total area under the greenhouse is

71.5 m2 with the dimensions as 5.6×13.5 m. the Experimental greenhouse

has 7 rows with 80 cm width. The frame of the greenhouse was fabricated

using Iron skewers. The distances between the skewers were fixed 1.5m

figure (3). The height of the greenhouse at the centre is 3.0 m. The

vertical of the side walls were 1.5 m. The greenhouse frame was covered

with a single polyethylene sheet of 200-mm-thickness.

2.2.2 Crops cultivation and irrigation system

Cucumber is one of the important vegetable crops in the world also in

Egypt. Cucumber plants were grown in Trays in the Arboretum for one

month and after that transferred to greenhouse in 20 November 2009,



placed at 0.80 m spacing between the rows and 0.40 m within a row. The

number of cucumber plants in the greenhouse 225 (3.125 plant/m2)

Abdelmenim (1998). The optimum temperature required for the plants

was in the day about 20-24oC and in the night about 15-18

oC according to

Abdelmenim (1998).

Fig.3-a: Isometric view of the greenhouse used.

Fig.3-b: Elevation of the greenhouse used in the experimental study.

2.2.3 Heat Exchanger

The heat exchanger is designed to remove heat from the exhaust gas of an

engine and transfer it to the greenhouse. It is the most equipment

commonly used to heat the greenhouse.

2.2.4 The experimental Engine



The engine used in this study was a 5 HP Water Cooled Diesel Engine.

The engine is of the 553cm3, single cylinder type with overhead valves.

The combustion chamber is cylindrical in shape with the compression

ratio of 17:1. The four-stroke, naturally aspirated, water-cooled,

compression ignition engine is nominally rated at 3.7 kW at 1500 rpm and

25Nm of torque at 1900 rpm. Biogas was supplied through a plastic pipe

and mixed with inlet air from the engine filter air.

2.3 Measurements

2.3.1 Solar radiation

Pyranometers CM 6 was used to measure the solar irradiation outside the

greenhouse which fixed in a height of 2.5 m.

2.3.2 Temperatures

The air temperature inside greenhouse, air temperature outside

greenhouse, soil temperature, plant temperature and cover temperature

were measured using IC (LM35) sensors. The data collection and

recording frequency were recorded every 5 seconds and 1 hour average of

each measurement by using a LabJacks data logger.

2.3.3 Relative humidity

To measure the inside and the outside humidity, aspirated psychrometers

which have been developed at the institute of Horticulture and

Agricultural Engineering, Hannover University, were used.

RESULTS AND DISCUSSION

The results of the modell validation were discussed under the following

heads:

3.1 -Greenhouse air temperature

The calculated temperatures of inside air greenhouse using the computer

model along with arithmetic average of measured values at different time

of the day are shown in figure (4). The air temperatures inside greenhouse

fluctuated with the daily amplitude becoming larger at the noon. It

reached the peak at noon and declined in late afternoon and early

morning. The air temperature inside the closed greenhouse reached the



maximal values were 36.92 and 38.5 oC in January and February and the

minimum value were 13.59 and 13 oC in January and February.

predicted and measurement Inside air temperature

10

15

20

25

30

35

40

45

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

Insid

e a

ir t

em

pera

ture

[ o

C]

air predicted Janaury air measurement Janaury

air predicted February air measurement February

Fig.4: predicted and measured inside air temperature of the

greenhouse.

Residuals of inside air temperature

-4

-3

-2

-1

0

1

2

3

4

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

Resid

uals

[ o

C]

air Residuals January

air Residuals February

Fig.5: Residuals of the measured and predicted inside air

temperature.

It can be observed that, the maximum difference between measured and

predicted temperature was 3.59 oC in January figure (5). The minimum

correlation coefficient between values was 0.970 in February figure (6).



2-6 January R2 = 0.9773

10

15

20

25

30

35

40

10 15 20 25 30 35 40

Measured inside air temperature, oC

Pre

dic

ted ins

ide a

ir

tem

pera

ture

, oC

2-6 February R2 = 0.9705

10

15

20

25

30

35

40

10 15 20 25 30 35 40Measured inside air temperature, oC

Pre

dic

ted in

sid

e a

ir

tem

pera

ture

, oC

Fig.6: Comparison between measured and predicted of the inside air

temperature.

And there is a correspondence between the simulated and the measured

air temperatures inside the greenhouse. The air temperature inside

greenhouse is influenced by air temperature outside the greenhouse,

incident global solar radiation and heating system.

3.2 Greenhouse plant temperature

Figure (7) present the simulation results obtained from the model during

the simulation periods and the measurement in the same time. The plant

temperature inside the closed greenhouse reached 37.17 oC in January,

while it is 36.3 oC in February. The minimum value was 13.57

oC in

January, while it was 14.1 o

C in February. The trend of the curve of

calculated values as well as experimental value of plant temperature is

similar. It increases from morning with increase in time and reaches

maximum value at about 12 am and then decreases. It can be observed

that, the maximum difference between measured and predicted

temperature was 4.1 oC in January figure (8). The minimum correlation

coefficient between values was 0.977 in January figure (9).

Further, results show that the calculated values of plant temperature are

matching very well with the measured experimental values.



predicted and measurement

Plant temperature

10

15

20

25

30

35

40

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

Pla

nt

tem

pera

ture

[ o

C]

plant predicted Janaury plant measurement Janaury

plant predicted February plant measurement February

Fig.7: predicted and measured plant temperature.

Residuals of Plant temperature

-4

-3

-2

-1

0

1

2

3

4

5

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

Resid

uals

[ o

C]

Plant Residuals January Plant Residuals February

Fig.8: Residuals of the measured and predicted plant temperature.

2-6 January R2 = 0.9778

10

15

20

25

30

35

40

10 15 20 25 30 35 40Measured plant temperature, oC

Pre

dic

ted p

lant

tem

pera

ture

, oC

2-6 February R2 = 0.9783

10

15

20

25

30

35

40

10 15 20 25 30 35 40

Measured plant temperature [oC]

Pre

dic

ted p

lant

tem

pera

ture

[oC

]

Fig. 9: Comparison between measured and predicted of the plant

temperature.



3.3 Greenhouse cover temperature

The cover is the important element in the greenhouse construction for

Keeping of the energy. Temperature of the cover is an essential

parameter needed for any analysis of energy transfer in the greenhouses

technology. The energy transfer to inside greenhouse from the cover in

the day time and in the night the energy transfer from the greenhouse to

the outside air because of the variation in the inside air temperature. For

this, it is observed; that the cover temperature during sunshine hours is

higher than the room temperature, whereas the trend is reversed during

night hours. The predicted temperatures of cover of greenhouse using the

computer model along with measured values at different time of the day

are shown in figure (10). Similarly, simulations data were compared with

measurements at tow periods of 5 consecutive days.


cover temperature

10

15

20

25

30

35

40

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

cover

tem

pera

ture

[ o

C]

cover predicted Janaury cover measurement Janaury

cover predicted February cover measurement February

Fig. 10: predicted and measured cover greenhouse temperature.

Figure (10) presents the simulation results obtained from the model

during the simulation periods and the measurement in the same time. The

cover temperature reached to the maximal value was 37.87 oC in January,

while it was 36.13 oC in February. And the minimum values were 12.77

oC in January, while it was 13.24

oC in February. It can be observed that,

the maximum difference between measured and predicted temperature

was 3.8 oC in February figure (11).



Residuals of Cover temperature

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

Resid

uals

, oC

Cover Residuals January Cover Residuals February

Fig.11: Residuals of the measured and predicted cover temperature.

2-6 January R2 = 0.9854

10

15

20

25

30

35

40

10 15 20 25 30 35 40Measured cover temperature, oC

Pre

dic

ted c

over

tem

pera

ture

, oC

2-6 February R2 = 0.9708

10

15

20

25

30

35

40

10 15 20 25 30 35 40

Measured cover temperature, oC

Pre

dic

ted c

over

tem

pera

ture

, oC

Fig.12: Comparison between measured and predicted of the cover

temperature.

The minimum correlation coefficient between values was 0.970 in

February figure (12). There is a correspondence between the simulated

and the measured cover temperatures.

3.4 Greenhouse soil temperature

A popular and economical heat storage material is the soil. Sensible heat

storage (with air as the energy transport mechanism) placed underground

have the advantage of providing a large and cheap heat transfer surface.

Where the heat is absorbed through the cover during the period of the

brightness of the sun all day long, then a reverse process occurs during

the evening ( the soil surface works as a heat exchanger), which retrieves



the most of the heat absorbed during the day and thus help in heating the

greenhouse.


soil temperature

10

15

20

25

30

35

40

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

Soil

tem

pera

ture

, oC

soil predicted Janaury soil measurement Janaury

soil predicted February soil measurement February

Fig.13: predicted and measured soil temperature.

Residuals of Soil temperature

-4

-3

-2

-1

0

1

2

3

4

0 12 24 36 48 60 72 84 96 108 120 0 12 24 36 48 60 72 84 96 108 120

Time, h

Resid

uals

, oC

Soil Residuals January Soil Residuals February

Fig.14: Residuals of the measured and predicted soil temperature.

Figure (13) show the time evolution of the simulated and measured soil

surface temperatures for 10 successive days. It was observed that the soil

surface temperature fluctuated and increased over time from January until

February and the soil temperature reached the maximal value was 36.64 oC in January, while it was 36.4

oC for February. And the minimum

values were 16.3 oC in January, while it was 15.8

oC in February. It can

be observed that, the maximum difference between measured and

predicted temperature was 4.32 oC in January figure (14). The minimum

correlation coefficient between values was 0.975 in January figure (15).



And there is a correspondence between the simulated and the measured

soil temperatures inside the greenhouse. The soil temperature inside

greenhouse is influenced by air temperature outside the greenhouse,

incident global solar radiation, heat capacity of the soil, conductivity of

the soil and heating system.

2-6 January R2 = 0.9754

10

15

20

25

30

35

40

10 15 20 25 30 35 40

Measured soil temperature, oC

Pre

dic

ted s

oil

tem

pera

ture

, oC

2-6 February R2 = 0.9772

10

15

20

25

30

35

40

10 15 20 25 30 35 40

Measured soil surface temperature [oC]

Pre

dic

ted

so

il s

urf

ace

tem

pe

ratu

re [

oC

]

Fig.15: Comparison measured and predicted of the soil temperature

3.5 The Relative Humidity.

The trend of the curve of calculated values in line with experimental

values of relative humidity of inside air is similar but not good degree. It

decreases from morning with increase in time and reaches minimum at

about 2 pm and then increases. The relative humidity inside the

greenhouse reached the maximal value were 96.2 % in January, while it

was 87.36 % for February. And the minimum values were 66.11 % in

January, while it was 63.88 % for February.

Prediected and Measurement of the Relative Humidity

50556065707580859095

100

0 30 60 90 120 150 0 30 60 90 120 150

Time, min.

Rela

tive H

um

idity %

RH predicted Janaury RH measurement JanauryRH predicted February RH measurement February

Fig.16: predicted and measured relative humidity.



Figure (16) represents the differences between the measured and the

predicted values of the inside relative humidity % during the simulation

periods. The maximum differences between measured and predicted

values profile are 9 % in January, while it was 6.31 % for February. The

minimum correlation coefficient between values was 0.818 in January

figure (17).

2-Janaury R2 = 0.8187

60

65

70

75

80

85

90

95

100

60 65 70 75 80 85 90 95 100

Measured Relative Humidity %

Pre

dic

ted

Re

lative

Hu

mid

ity %

2- Febraury R2 = 0.8831

60

65

70

75

80

85

90

60 65 70 75 80 85 90

Measured Relative Humidity %

Pre

dic

ted

Re

lative

Hu

mid

ity %

Fig.17: Comparison between measured and predicted of the relative humidity.

CONCLUSION

1-Using waste heat as an input for greenhouse operations is a new

mechanism for reducing operating costs.

2- As a whole, a good agreement between the predicted and measured

values was obtained during the entire modelling period. This means that

the model can be used to predict a thermal performance of the greenhouse

elements in a wide range of solar radiation and temperatures.

REFERENCES

Abd el Menem, A. (1998). Protected cultivation technology

(GREENHOUSE)

Amon, T.; Amon, B. and Kryvoruchko, V. (2007). Methane production

through anaerobic digestion of various energy crops grown in

sustainable crop rotations Bioresource Technology 98 :3204–3212

Boulard, T.; Razafinjohany, E.; Baille, A.; Jaffrin, A. and Fabre, B.

(1990). Performance of a greenhouse heating system with a phase

change material. Agricultural and Forest Meteorology 52, 303–318.



EL Sheikh, I.H. (2001).soil heating and climate simulation model for

greenhouses. Ph.D. Thesis, University of Hannover, Germany.

Gautam, R.; Baral, S. and Heart, S. (2007). Biogas as a sustainable

energy source in Nepal: Present status and future challenges

Renewable and Sustainable Energy Reviews(2007),

doi:10.1016/j.rser.2007.07.006

Harmanto; Tantau1, H.J. and Salokhe, V.M.(2006). Microclimate and

Air Exchange Rates in Greenhouses covered with Different Nets in

the Humid Tropics Biosystems Engineering (2006) 94 (2), 239–253

doi:10.1016/j.biosystemseng.2006.02.016

He, J. ; Hoyano, a. and Asawa, T. (2009). A numerical simulation tool for

predicting the impact of outdoor thermal environment on building

energy performance. Applied Energy, 85: 1595-1505

Kumari, N.; Tiwari, G.N. and Sodha, M.S. (2003). Modelling of a

greenhouse with integrated solar collector for thermal heating.

International Journal of Ambient Energy 27 (30), 125–136.

Lewis, M. J. (1990). Physical properties of foods and food processing

systems. Ellis Horwood Limited.

Mutwiwa, U. N. (2007). Effects of Different Cooling Methods On

Microclimate and Plant Growth in Greenhouses In The Tropics.

Ph.D. Thesis, University of Hannover, Germany.

Oeztuerk, H.H. and Ba-s-cetin-celik, A. (2003). Energy and Exergy

Efficiency of a Packed-bed Heat Storage Unit for Greenhouse

Heating Biosystems Engineering (2003) 86 (2), 231–245

Oeztuerk, H.H. (2005). Experimental evaluation of energy and exergy

efficiency of a seasonal latent heat storage system for greenhouse

Seginer, I. and Albright Louis, D. (1980). Rational operation of

greenhouse thermal-curtains. Transactions of the ASAE 1980:1240–

45.

Shukla, A.; Tiwari, G.N. and Sodha, M.S. (2006). Thermal modeling for

greenhouse heating by using thermal curtain and an earth–air heat



exchanger Building and Environment 41 (2006) 843–850

Singha, G.; Parm Pal Singhb, P.; Lubanaa, P.P. S. and Singh K.G (2006).

Formulation and validation of a mathematical model of the

microclimate of a greenhouse Renewable Energy 31 :1541–1560

Strauch, K.-H. (1985). Geschlossene Gewächshaussysteme mit

integrierter solarer Wasserentsalzungsanlage für aride Gebiete.

Gartenbautechnische Informationen 22, Universität Hannover.

Taha, A. T.; Eissa, A. H.; Gamea, G.R. and Hidarh, H. M. (2009).

Simulation model of flat plat solar collector performance. In the 1 St

Scientific conference for marketing the applied university research,

Minoufiya University, Egypt, (pp. 421-438), 7-8 October, 2009.

Taha, A.T. (2003). Simulation Model of Energy Fluxes in Passive Solar

Greenhouses with a Concrete North-Wall. Ph.D. Thesis, University

of Hannover, Germany.

Tantau, H.-J. (1983). Heizunganlagen im Gartenbau. Ulmer, Stuttgart.

Tantau, H.-J. (1998). Greenhouse climate – overview. Modelling,

Control and Optimization greenhouse, drying and Farm Energy

System.

Tiwaria, G. N.; Akhtarb, M. A.; Shuklaa, A. and Emran Khan, M.

(2006). Annual thermal performance of greenhouse with an earth–

air heat exchanger: An experimental validation Renewable Energy

31 (2006) 2432–2446

Von Elsner, B. (1982). Das Kleinklima der Wärmeverbrauch von

Geschlossenen Gewächshäusern „Ein Simulationsmodell zur

Gartenbautechnischen Bewertung unterReferences132

Berücksichtigung des Einflusses von Standortklima,

Pflanzenbestand undGewächshauskonstruktion.

Gartenbautechnische Informationen 12, Universität Hannover. Cited

from EL Sheikh, I.H. (2001).soil heating and climate simulation

model for greenhouses. Ph.D. Thesis, University of Hannover,

Germany .

Willits, D.H.; Marbis, J. M. and Cheng, J. (2003). Waste Heat Utilization

in a Greenhouse Used for the Removal of Nutrients from a Swine

Waste Stream



الولخص العربى

لتذفئت الصوة السراعيه ببستخذام حرارة غبزاث العبدم النبتجه هوديل ريبضى

هن هحرك يعول بوقود البيوجبز

د/ جوبل رشبد جبهع*

د/ هحوذ عبذ الفتبح عبذ الوقصود *

م.م/ هحوذ نبيه بيوهى عور **

حبص١ ف ظ ازرفبع عدد اصثبد اصزاع١ احدح ا ازم١بد اصزاع١خ ف إزبج ا

ازغ١١ككساد ابة١ككخ احب١كك ازكك ادد اكك رجفكك١ط اقزككبج فكك احمكك اى كك سككىب الككب

اقزرفبع اىج١س ف اسلبز اجعبز. بن الد٠د غسق اسزجد ف ردفئ اصكة. ىك

حككسن د٠ككصي ٠لكك ثلككد جفككط رىككب١ت ازدفئكك ركك اسككزجدا احككساز افمككد غككبشاد الككبد

اج١خبش ذه لاسزفبد ر اطبل ادز ف ردفئخ اصكث اصزاع١ك.زحم١ك كرا اكد

ر رص١ د٠ ز٠بظ زدفئخ صث شزاع١ ثاسكخ اكبشاد الكبد حكسن د٠كصي ٠لك ثلكد

و١ احكساز اعكبف اج١خبش. ٠زى اد٠ دع البدقد اس٠بظ١ از رحدد

افمد ىلا ىبد اصث رحذ ادزاس از ر ااء اكداة صكث اغطكبء

اجككبد ازسثكك وككره اسغثكك اسككج١ داةكك اصككث ركك وزبثزككب حككب ثاسككطخ ثسككبح

سازح وكك عبصككس اككبرلاة. ٠سككزد ككرا ازح١كك عكك رككاش اطبلكك ح١ككح ٠ككز حسككبة دزخككخ حكك

اصث اجزف ثبءا ع فسق و١خ اطبل اعبف افمد رحذ ظس دزاس١ حدد.

زككس 5.5زبوككد كك صككحخ اد٠كك ركك رحم١مكك ردس٠ج١ككب ذككه ثزصكك١ صككث شزاع١كك اثلبدككب

ع زس غي فك لس٠كخ اصكطجبز سوكص كج١ اىك حبفنكخ اف١ك ازك رمك 5..5× عسض

3. 55ع ةػ عسض بي ةػ اقسزاء ر شزاعزب ثحصي اج١بز ف افزكس ك كس

حصككب 5ركك رككدفئزب ثغككبشاد عككبد حككسن د٠ص٠كك لدزركك 9353حزكك ككبزض 9332ككفجس

داةك اصكث. رثج١ز١ىب١ى. ر رجس٠د ابشاد البد ردفئخ اصث ثاسطخ جبدي حساز ر

حسازح ولا ااء اداة صث اغطبء اجبد ازسث اسغثك اسكج١ ر ل١بض دزخ

ثكا رك عك زسكػ مك١ وك 5داة اصث ةلاي فزكسح ادزاسك.ر رسكد١ اج١بكبد وك

بمبسكك وبككذ اكك ازككبحح ازحصكك ع١ككب كك الكك لكك١ ث ركك مبزككخ ازككبحح احسككثسككبع

..3.2 3.2.3 3.2.3رجككبغ ثكك١ وككلا كك اج١بككبد احسككث امبسكك كك لبكك اقز

ااء اغطبء اجبد ازسث عك ازسر١كت. الك دزخكخ حكساز ىلا 3.050 3.2.5

ككك اككاء اغطككبء اجكككبد دزخككك ئ٠كك ىككلا 55.0 .5..5 ...59 .5كك كك

خ١د ث١ ام١ امبسك احسكث لاي ازبحح ر احصي ع ارفبقازسث ع ازسر١ت. ة

داء احكساز صكث شزاع١ك ثكبقاذج زجؤ را ٠ل أ ٠ى اسزجدا .زدسثةلاي فزسح ا

.ى دعخ البصس اجزف ثبقظبف ا اق لبع ا س حدح ازدفئ

جبهعت الونوفيه -قسن الهنذسه السراعيه -اعيه الوسبعذ استبر الهنذسه السر*

جبهعت الونوفيه -قسن الهنذسه السراعيه -هذرش هسبعذ **

MATHEMATICAL MODEL FOR GREENHOUSE HEATING BY …

Documents

Transcript of MATHEMATICAL MODEL FOR GREENHOUSE HEATING BY …